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Paper   IPM / Physic / 6530
School of Physics
  Title:   Hamiltonian Systems on Quantum Spaces
  Author(s):  A. Shafei Deh Abad
  Status:   Published
  Journal: J. Phys. A: Math. Gen.
  No.:  28
  Vol.:  31
  Year:  1998
  Pages:   4795-4803
  Supported by:  IPM
  Abstract:
In this paper we first characterize the Lie algebra of derivations of the three-dimensional Manin quantum space as the semi-direct product of the Lie algebra of its inner derivations and the threefold generalized Virasoro algebra with central charge zero. Then we consider Hamiltonian systems on the quantum plane and we prove that the set of Hamiltonian derivations is a Virasoro algebra with central charge zero. Moreover, we show that the only possible motions on the quantum plane come from quadratic Hamiltonians and we find the solutions of the corresponding Hamilton equations explicitly.

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